Logo by reallybigname - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Visit the official fractalforums.com Youtube Channel
 
*
Welcome, Guest. Please login or register. March 28, 2024, 05:50:53 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: 1 [2]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Pertubation and 3rd degree Mandelbrot  (Read 1975 times)
0 Members and 2 Guests are viewing this topic.
knighty
Fractal Iambus
***
Posts: 819


« Reply #15 on: May 13, 2014, 08:59:51 PM »

So you did 7th degree by hand!  shocked Impressive! and looks good.  smiley
Logged
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


WWW
« Reply #16 on: May 14, 2014, 12:31:08 AM »

lol, dudes, very amazing work, any chance for creatung pertubation optimization in an "automated" way !??!
i think i comes down to symbolic problem sovling .... we all know computers can do such, although it might be a little frightening, but isnt that we made computers for !?
so, perhaps ... formulate it in a mathematica kind of way, in a way that it can be solved automatically for any (lol, non integer, non real  ) exponent

and, dudes, you know why i am askin ? it is just because hybridisation techniques like alternations, could really really really be enlighted by that, because we have not yet deeply zoomed the easiest of the pertubations, like alternating a 2 and a 3 exponent mandelbrot together cheesy ...

just dreaming ahead .... those damn computer slaves are made for such things, arent they !?

Logged

---

divide and conquer - iterate and rule - chaos is No random!
knighty
Fractal Iambus
***
Posts: 819


« Reply #17 on: May 14, 2014, 08:49:48 PM »

That's what I'm still dreaming of too. Not only for 2D escape time fractals but also for 3D ones. Yes, it possible... but difficult to code for one person alone . That would be a good collaborative work.
IMHO, the main issue is mantaining good performance while having the ability to set custom formulas. AFAIK, LLVM is the only tool that is powerful enought for the job but it's heavy, very heavy.  hurt
Another solution would be to use plugins just like mandelbulb3D or apophysis.

@Kalles Fraktaler:
In case it will be useful for series approximation for higher power MB sets, here is the "general" formula of the derivatives (p>=3):
X_{n+1}=X_n^p+X_0
X_{n+1}'=p X_n^{p-1} X_n' + 1
X_{n+1}''=p X_n^{p-2} ((p-1) X_n'^2 + X_n X_n'')
X_{n+1}'''=p X_n^{p-3} ((p-1) X_n' ((p-2) X_n'^2 + 3 X_n X_n'') + X_n^2 X_n''')

It becomes more and more cumbersome for higher derivatives (there is a structure though).
Logged
Kalles Fraktaler
Fractal Senior
******
Posts: 1458



kallesfraktaler
WWW
« Reply #18 on: May 15, 2014, 01:57:21 PM »

Thanks knighty, I will examine these to see if they can yield more iterations.

Formula interpretation and derivation... yeah, that would be something  shocked

I received an interesting suggestion to implement PSA on the formula Xn+1=Xn(1/Xn)+X0
But I currently don't know how to make fractional power of complex number or derivative them...smiley
Logged

Want to create DEEP Mandelbrot fractals 100 times faster than the commercial programs, for FREE? One hour or one minute? Three months or one day? Try Kalles Fraktaler http://www.chillheimer.de/kallesfraktaler
http://www.facebook.com/kallesfraktaler
Kalles Fraktaler
Fractal Senior
******
Posts: 1458



kallesfraktaler
WWW
« Reply #19 on: May 16, 2014, 11:03:49 AM »

Unfortunately no more iterations could be skipped using 3 terms on 4th power Mandelbrot, compared to using 1 term.
Thanks anyway!
Logged

Want to create DEEP Mandelbrot fractals 100 times faster than the commercial programs, for FREE? One hour or one minute? Three months or one day? Try Kalles Fraktaler http://www.chillheimer.de/kallesfraktaler
http://www.facebook.com/kallesfraktaler
therror
Explorer
****
Posts: 42


« Reply #20 on: November 15, 2016, 03:56:18 PM »



Has anyone used perturbation theory for arbitrary (non-integer) power?
Logged
Kalles Fraktaler
Fractal Senior
******
Posts: 1458



kallesfraktaler
WWW
« Reply #21 on: November 15, 2016, 05:07:03 PM »


Has anyone used perturbation theory for arbitrary (non-integer) power?
Has anyone implemented arbitrary precision at all for arbitrary non-integer power?
To calculate power on complex numbers since and cosine is involved, and for arbitrary power, Taylor series would be needed, which involves iterations. Iterations on iterations. I imagine it would be incredible slow?

That's what I'm still dreaming of too. Not only for 2D escape time fractals but also for 3D ones. Yes, it possible... but difficult to code for one person alone . That would be a good collaborative work.
IMHO, the main issue is mantaining good performance while having the ability to set custom formulas. AFAIK, LLVM is the only tool that is powerful enought for the job but it's heavy, very heavy.  hurt
Another solution would be to use plugins just like mandelbulb3D or apophysis.

@Kalles Fraktaler:
In case it will be useful for series approximation for higher power MB sets, here is the "general" formula of the derivatives (p>=3):
<Quoted Image Removed>
<Quoted Image Removed>
<Quoted Image Removed>
<Quoted Image Removed>

It becomes more and more cumbersome for higher derivatives (there is a structure though).
Knighty, your general formula works like a charm.
Would it be possible to make arbitrary number of terms as well?
Logged

Want to create DEEP Mandelbrot fractals 100 times faster than the commercial programs, for FREE? One hour or one minute? Three months or one day? Try Kalles Fraktaler http://www.chillheimer.de/kallesfraktaler
http://www.facebook.com/kallesfraktaler
Pages: 1 [2]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Third degree polynomial fractals Let's collaborate on something! stigomaster 3 2765 Last post November 16, 2009, 10:24:24 PM
by kram1032
A degree 4/2 rational function Mandelbulb Renderings BradC 9 2613 Last post December 17, 2009, 08:43:31 PM
by BradC
Help: Mandelbrot pertubation fails when zooming deeper than 1E1400 Programming CFJH 10 1130 Last post January 08, 2014, 06:55:10 PM
by Kalles Fraktaler
Pertubation Theory Glitches Improvement Announcements & News « 1 2 ... 5 6 » Pauldelbrot 82 27828 Last post January 07, 2017, 07:37:03 AM
by quaz0r
360 degree animation inside a 360 degree panorama Movies Showcase (Rate My Movie) edufrick 2 1319 Last post December 05, 2015, 02:12:14 PM
by Caleidoscope

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.269 seconds with 24 queries. (Pretty URLs adds 0.012s, 2q)